So \( f_{\alpha , \beta } =[\alpha \lambda , \beta \lambda ] \) .
Let \(\omega = \beta \alpha ^{-1}\) . It was shown in [1]} that \(\alpha \Phi _\omega \)  extends \(f_{\alpha , \beta }\)  where
\(\Phi _{\omega }(s,p):= \frac{s/2 + \omega p}{1+ \omega s/2}.\) 
